We use the same setting for different sizes RevCol models on MIM pre-training. The hyper-parameters generally follow [4, 2]. Table 3 shows the detail training settings after MIM pre-training. We also show training settings on ImageNet-1K after ImageNet-22K fine-tuning. For semantic segmentation, we evaluate different backbones on ADE20K dataset.

So from this viewpoint, the Schedule-Free updates can be seen as a version of momentum that has the same immediate effect, but with a greater delay foradding intheremainder ofthegradient.

We introduce Evolution Guided General Optimization via Low-rank Learning (EGGROLL), an evolution strategies (ES) algorithm designed to scale backprop-free optimization to large population sizes for modern large neural network architectures with billions of parameters. ES is a set of powerful blackbox optimisation methods that can handle non-differentiable or noisy objectives with excellent scaling potential through parallelisation. Na{ï}ve ES becomes prohibitively expensive at scale due to the computational and memory costs associated with generating matrix perturbations $E\in\mathbb{R}^{m\times n}$ and the batched matrix multiplications needed to compute per-member forward passes. EGGROLL overcomes these bottlenecks by generating random matrices $A\in \mathbb{R}^{m\times r},\ B\in \mathbb{R}^{n\times r}$ with $r\ll \min(m,n)$ to form a low-rank matrix perturbation $A B^\top$ that are used in place of the full-rank perturbation $E$. As the overall update is an average across a population of $N$ workers, this still results in a high-rank update but with significant memory and computation savings, reducing the auxiliary storage from $mn$ to $r(m+n)$ per layer and the cost of a forward pass from $\mathcal{O}(mn)$ to $\mathcal{O}(r(m+n))$ when compared to full-rank ES. A theoretical analysis reveals our low-rank update converges to the full-rank update at a fast $\mathcal{O}\left(\frac{1}{r}\right)$ rate. Our experiments show that (1) EGGROLL does not compromise the performance of ES in tabula-rasa RL settings, despite being faster, (2) it is competitive with GRPO as a technique for improving LLM reasoning, and (3) EGGROLL enables stable pre-training of nonlinear recurrent language models that operate purely in integer datatypes.

Recently, Zamani and Glineur (2023) and Defazio et al. (2023) showed that the exact worst-case Our approach uses an alternative form of momentum that replaces traditional momentum. So from this viewpoint, the Schedule-Free updates can be seen as a version of momentum that has the same immediate effect, but with a greater delay for adding in the remainder of the gradient.

Symbol Definition x 2X,u 2U,y 2Y Input, model output, and desired output p ( x, y) Joint probability distribution of input x and target or label y f: X!U, 2 Model function with parameters in parameter space L ( p, f):( p, f) 7! R